Energy and Human Ambitions on a Finite Planet, 2021a

9 Climate Change 151
ways that we are not close to fully underst<strong>and</strong>ing. Climate change messes
with the system in such a way to prevent accurate prediction of the
long-term consequences of one species or another disappearing from
the web of life.
The consequences of climate change are elaborated in many sources that
are not difficult to find. Rather than try to add to the general awareness,
this section—in the spirit of the book—aims to provide students with
some tools 40 to be able to quantitatively underst<strong>and</strong> how the physical
world reacts to changes in radiative forcing. Specifically, we concentrate
on the process of heating up 41 elements of the planet, <strong>and</strong> on sea level
rise.
40: . . . <strong>and</strong> make connections to earlier content
41: For amusement, try substituting the
phrase “climate change” with “hotting up.”
9.4.1 Heating Up
Recall that the radiative forcing of 2.2 W/m 2 arising from a 50% enhancement
to the pre-industrial CO 2 concentration 42 is expected to result in
1.7 ◦ C of eventual warming. But measurements indicate only 1.0 ◦ C of
warming so far. Is our underst<strong>and</strong>ing wrong?
As we saw in Sec. 6.2 (p. 85), it takes energy to change something’s
temperature. When the rate of energy input 43 is limited, it takes time to
accomplish a temperature rise. 44
Earth is by-<strong>and</strong>-large in thermodynamic equilibrium. The sun deposits
energy onto Earth at a rate of 240 W/m 2 , when averaged over the surface
(Eq. 9.3). Prior to the modern increase in CO 2 concentration, we had
no additional radiative forcing from CO 2 <strong>and</strong> had an average surface
temperature of 288 K (15 ◦ C), as in Eq. 9.4. Because it was in equilibrium,
we know that the infrared radiation from Earth must have also totaled
240 W/m 2 to match the solar input.
42: . . . from 280 ppm v to 420 ppm v
43: . . . which we know as power
44: A burrito in the microwave does not
heat up instantly, for instance.
sun
240
90 150
GHG: 0.77
240
sun
240
86 152
GHG: 0.78
238
sun
240
83 156
GHG: 0.79
239
sun
240
80 160
GHG: 0.80
240
390
150
390
152
395
156
400
160
288 K
288 K
289 K
289.8 K
pre-industrial equilibrium
add CO 2
: 2 W/m 2 imbalance
adjusting: 1 W/m 2 imbalance
post-CO 2
equilibrium
Figure 9.15: Four steps to illustrate (in a grossly simplified way) the process of Earth adapting to an increase in greenhouse gas (GHG).
Starting from the left within each panel, solar input is held constant at 240 W/m 2 . Most of the radiation leaving the ground—quantitatively
adhering to σT 4 —is absorbed by GHGs (fraction absorbed indicated in GHG “cloud”), the rest escaping directly to space. Half the
absorbed energy is radiated up (escaping) <strong>and</strong> half back down. The dashed arrow at right is the net radiation escaping. Integer numbers
are in W/m 2 , <strong>and</strong> arrow widths are scaled accordingly. Ground temperature is indicated at bottom. See text for narrative sequence.
Figure 9.15 sums up the story. 45 The first panel shows the pre-industrial
equilibrium condition, in which 77% of the infrared radiation from the
ground was intercepted by the greenhouse gases, while 23% (90 W/m 2 )
45: Note that in each panel, adding the
two top arrows or subtracting the two bottom
ones both yield the same number—
matching the dashed arrow on the right.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.